This PDF file contains the editorial “Editorial: People and Places (SPIE’s 50th Year)” for OE Vol. 44 Issue 07

We present the principle, fabrication, and characterization of a novel wavefront splitting intrinsic Fabry-Perot fiber temperature sensor. The sensor is made by splicing a section of fused silica tubing to the tip of a single-mode fiber. The completed sensor has the same diameter as the fiber and the sensor length is less than 0.5 mm.

We propose a holographic code for synthesis of fully-complex transmittance, which can be implemented employing a twisted-nematic liquid-crystal display, two linear polarizers, and a He-Ne laser. This simple setup provides a reduced phase range and amplitude modulation with significant variance. Our holographic code efficiently exploits this constrained modulation for the accurate encoding of arbitrary complex transmittance. Two experimental examples illustrate the good performance of the holographic code.

A folding nonblocking 4×4 optical matrix switch in simplified-tree architecture was designed and fabricated on a silicon-on-insulator wafer. To compress chip size, switch elements (SEs) were connected by total internal reflection mirrors instead of conventional S-bends. For obtaining smooth interfaces, potassium hydroxide (KOH) anisotropic chemical etching of silicon was employed. The device has a compact size of 20×3.2 mm² and a fast response of 8±1 µs. Power consumption of 2×2 SE and excess loss per mirror were 145 mW and –1.1 dB, respectively.

We demonstrate a 57.6-km-long linear photonic crystal fiber (PCF) transmission experiment using a recirculating loop with a 19.2-km PCF spool. A 10-Gbit/s non-return-to-zero signal was transmitted over PCF transmission fiber without dispersion compensation.

Classic mean-shift trackers have no integrated scale adaptation, which limits their performance in tracking variable scale objects. By analyzing the similarity of object kernel histograms, we found that the changes of object scale and position within the fixed kernel make the Bhattacharyya coefficient monotonic decreasing. The work plays a guiding role in solving scaling problems within the mean-shift framework.

This PDF file contains the editorial “Editorial: Academician Vladimir Evseevich Zuev—Scientist, Teacher, and Organizer” for OE Vol. 44 Issue 07

Water vapor transmission function calculations are performed in the case of nonhomogeneous atmospheric paths based on the exact formulas for the coefficients of expansion into the series of exponents that we obtained earlier. A comparison of the results obtained with the exact formulas and those obtained in the context of the correlated k distribution (CKD) approximation shows that the CKD approximation is successful due to the fact that the optical thicknesses are the real correlating values in the Earth atmosphere, whereas the differences in the absorption coefficient behavior for various thermodynamic conditions are not of great importance in this problem. Situations in which the CKD approximation may break down are pointed out. It is noted that the accuracy of the expansion into a series of exponents depends on the accuracy of the absorption coefficient corresponding to the abscissas of the quadrature formulas more than on the number of points. Cases are mentioned in which the CKD approximation gives results far from the line-by-line results, whereas a calculation that uses exact formulas works well in these cases.

The method of time-resolved photoacoustic spectroscopy is applied to study the weak aerosol absorption of shortwave radiation in the atmospheric air. Using synchronous measurements of aerosol light absorption coefficients by a pulsed photoacoustic spectrometer and mass concentration of black carbon by an Aethalometer, we determine the values of the efficiency σ of aerosol light absorption in the atmospheric air in the shortwave spectral range for three wavelengths: σ (0.532 µm)=(5.49±3.57)m² g^–1, σ(0.694 µm)=(4.46±2.61)m² g^–1, and σ(1.064 µm)=(2.87±1.84)m² g^–1. The experimental results are approximated by the spectral dependence σ(λ)=3.1λ–^0.92, where wavelength λ is expressed in micrometers. We discuss the calibration procedure for the pulsed photoacoustic spectrometer in studying the aerosol absorption.

The influence of minor H₂ and HBr additives on the generation characteristics of some copper bromide vapor lasers is experimentally investigated. It is demonstrated that at optimal concentrations of both admixtures, the average generation power increases by five times for lasers with small active element diameters, and by two times for lasers with major diameters. For the maintenance of an adjusted concentration of the admixture, the original construction of the HBr generator is developed, which in the reversible regime removes not only the HBr surplus from active volume of the laser, but also at least some of harmful products of the working laser. The obtained results are applied to the development of a sealed-off self-heating copper bromide vapor laser with an integral HBr generator, operating in the automatic regime.

We describe the algorithms for the simulation of cw and pulsed coherent Doppler wind lidar operation in a turbulent atmosphere and the methods to estimate the mean wind and the parameters of small-scale wind turbulence from lidar data. The algorithms are realized as LabView computer codes, which include parts simulating the atmospheric turbulent wind fields based on the Karman model, lidar signal, and data processing. The errors for lidar measurement of turbulent parameters and the retrieval of the wind vertical profiles are estimated based on a computer simulation of the coherent Doppler lidar system operation.

Possibilities of numerical amplitude demodulation for separating long-term changes in quasi-periodical geophysical series are discussed. The influence of long-term changes in the velocity of the zonal equatorial wind on some meteorological and hydrological phenomena is analyzed using the method proposed. The high efficiency of the proposed method of constructing regression models is substantiated.

This paper is a revision of a paper presented at the SPIE conference on Laser Radar Technology for Remote Sensing, Sep. 2003, Barcelona, Spain. The paper presented there appears (unrefereed) in SPIE Proceedings Vol. 5240. Light scattering by large, as compared to wavelength, ice crystal particles is considered within the framework of geometric optics. Certain general equations for the scattering matrices and for an averaging procedure over an arbitrary distribution of particle orientations are considered. The appearance of a strong backscattering peak is explained by the occurrence of right dihedral angles in the crystals. An analytical equation for the peak including the polarization properties is proposed.

The LOSA-MS combined small-sized single-wavelength backscatter lidar is described whose operation is based on the effects of Raman and elastic scattering. To extend the range of sounding, lidar returns are registered simultaneously in analog and photon counting regimes. A photodetector system for wavelength and polarization selection of lidar signals is described. The basic physical principles of laser sounding and methods of solving the lidar equation to retrieve information on the optical-physical state of examined objects are presented. Examples of using the LOSA-MS lidar for monitoring of spatiotemporal distribution of aerosol pollutants above an industrial center are given together with examples of investigation of the aerosol field structure under background atmospheric conditions.

Results of theoretical and experimental investigations of remote monitoring methods based on secondary radioactivity effects including anomalous gaseous fields and their emissions in optical and microwave ranges are discussed. The feasibility of remote registration of secondary emission and absorption spectra from weakly ionized regions in the atmosphere above nuclear power engineering objects, dumps, and tailings dumps of nuclear wastes are examined. Based on the literature data on the excess concentrations of aerosol and gaseous components produced in radiation fields above their background levels, the diffusion parameters of radioactive emissions in the atmosphere are evaluated. The methods under consideration are shown to be promising for ecological monitoring of atmospheric radioactive pollution. High sensitivities of these methods enable pollutants to be detected at long distances. Simultaneous use of passive and active methods gives additional information on the parameters of radioactive pollution.

Experimental data on seawater laser sensing with an airborne lidar having a changeable field of view are presented. Wind-driven sea waves and microwaves lead to Fresnel's splitting of a sounding beam into smaller sized beams, fluctuations, and escape of a number of signal photons from the detector field-of-view (FOV) cone, that is, to an apparent increase in the attenuation coefficient. Multiple scattering leads to the arrival of additional signal photons in the detector FOV, that is, to an apparent decrease in the attenuation coefficient. For the described lidar, two opposite processes provide its reliable operation at the FOV no less than 6 mrad.

The angle-resolved light scattering of several microrough silicon surfaces was measured with a laser reflectometer and presented in terms of the bidirectional reflectance distribution function (BRDF). The BRDF shows strong anisotropy and prominent subsidiary peaks for some surfaces, while it is nearly isotropic with a dominant peak for other surfaces. Similar characteristics can be observed in the microfacet orientation by analyzing the atomic force microscope (AFM) topographic data in the form of the two-dimensional (2-D) slope distribution function. A correlation has been constructed between the BRDF and the 2-D slope distribution. The salient features in the BRDF and the 2-D slope distribution are attributed to the modification of the surface of microfacets during chemical etching. This work shows that the angle-resolved light scattering measurements and the AFM topography measurement complement each other and provide important information about the microfacet orientation resulting from the wafer processing. The procedures described here can be used to obtain the slope distribution for a variety of microrough surfaces. This work will help the advancement of metrology in semiconductor wafer manufacturing.

Using a CO₂ laser as a heat source, carbon coatings have been successfully deposited on moving optical fibers in an open-air laser-induced chemical vapor deposition (LCVD) reactor. Applications include fusion splice recoat and in-line coating of optical fibers. The relationship between operating parameters and the carbon deposition temperature and rate was investigated. Results indicate that they are strongly dependent on the laser power density and the optical fiber's traverse velocity. In order to provide a deeper understanding of the fundamental principles that govern laser heating and the carbon LCVD processes, a heat transport model was developed to predict the fiber surface temperature during deposition. The surface temperatures obtained from experiments compared well with the predicted temperature. Based on the temperature calculations, various kinetic parameters, including the activation energy E_A and pre-exponential factor k₀ for the carbon deposition process, are determined. The optical fiber signal loss at 1550 nm induced by the LCVD process is observed to be less than 10^–3 dB at low laser power density.

A procedure is presented for the design of bilayer pellicle and bilayer-coated prism beam splitters that serve as the key optical element of the division-of-amplitude photopolarimeter (DOAP). The bilayer consists of two transparent thin films of sufficiently different refractive indices whose thicknesses are selected to achieve 50 to 50% split ratio and optimum ellipsometric parameters in reflection and transmission, such that the determinant of the DOAP instrument matrix is maximized at the proper angle of incidence. As a specific example, we present a Ge-coated nitrocellulose (NC) first-order pellicle beamsplitter for the near IR (2.0 to 2.2 µm). Visible designs include a GaP-coated NC fourth-order pellicle and a SiO₂-GaP bilayer-coated glass prism at and near the 633-nm wavelength. Operation of these beamsplitters over a range of incidence angles, wavelengths, and in the presence of ±5% film thickness errors is also considered.

Temporal decay of photon emission from avalanche photodiodes (APDs) is demonstrated. The steep rise of the reverse voltage can cause a higher probability of photon emission. For a silicon avalanche photodiode, the photon emission has a broad spectral distribution from 500 to 1100 nm with two peaks at 750 and 994 nm, respectively. The number of emitted photons increases by 44 Mcount/(s mA sr) as the APD's reverse current increases. This suggests that the reverse current, instead of the reverse voltage, applied to the APD is the main determinant of the photon emission. It is furthermore shown that the distribution of the photon emission is a super-Poisson distribution.

Near-degenerative near-collinear phase-match geometry for broadband optical parametric chirped-pulse amplification (OPCPA) at ≈ 780 nm is calculated in comparison with nondegenerate noncollinear phase-match geometry. In an experiment on LBO-I near-degenerate near-collinear OPCPA, high gain with broad gain bandwidth (≈71 nm, FWHM) at ≈ 780 nm is achieved by using an ≈ 390-nm pumping pulse. The stretched broadband chirped signal pulse near 780 nm is amplified to ≈ 412 µJ with a pumping energy of ≈ 15 mJ, and the total gain is <3.7×10⁶, which agrees well with the calculation. For a broadband (covering ≈ 100 nm) chirped signal pulse, the theoretical gain bandwidth has been attained experimentally for the first time.

The lasing wavelength of a single-section distributed feedback (DFB) laser diode can be modulated by modulating the drive current. This makes it possible to utilize the DFB laser diode in a frequency-modulated continuous wave (FMCW) range and velocity measuring system. In FMCW, the frequency of the laser is ramped, and the frequency difference between the reflected wave and a local-oscillator wave is monitored. For maximum performance the frequency ramping should be linear. Due to thermal phenomena, a linear ramping of the current seldom results in a linear ramping of the optical frequency. We have derived a discrete thermal model, using resistors and capacitors, of our laser module. The thermal model was then used as a starting point to model the frequency behavior of the laser and to derive modulation currents that resulted in a linear frequency ramping at some different modulation frequencies.

We report the temperature-independent measurement of displacement based on the chirp tuning of a fiber grating and a specially designed cantilever. The 3-dB bandwidth of the chirped grating changes linearly with displacement and is independent of the temperature. The displacement can be monitored directly by measuring the reflected light from the chirp grating. A linear displacement response of 37.063 mV/mm was obtained. The fluctuation of the output signal is less than 5% for a temperature range from 20 to 60°C without any temperature compensation technique. The sensor has potentially low cost due to its simple structure.

Based on formulas presented for the amplitude coupling ratio and the transfer function, transmission characteristics are analyzed and parameters are optimized for a polymer cross-grid array of microring resonant wavelength multiplexers around the central wavelength of 1.550918 µm with wavelength spacing 1.6 nm. In the design of the device, by means of selecting a resonant order m=95 and introducing a resonant order increment of adjacent filter elements Δm=2, we increase the ring radius difference of adjacent filter elements ΔR from 17 nm (for the case of Δm=0) to 337 nm. Calculated results show that the 3-dB bandwidth is about 0.2 nm, the ratio between the –1- and –10-dB bandwidths is about 0.22, the insertion loss is less than 0.5 dB, and crosstalk is below –39 dB for each of the eight horizontal output channels.

We aim to optimize the Hamiltonian algorithm for fiber alignment by simulation and experiments. We develop (1) a three-step optimization method to adjust two relevant parameters in the Hamiltonian algorithm in order to effectively make the alignment process faster and more stable, and (2) two methods to terminate Hamiltonian searching in order to preserve successful alignments under the influence of noise. We demonstrate the effectiveness of all these practical methods through experiments using an alignment system.

This paper is a revision of a paper presented at the SPIE Conference on Micro-Optics, VCSELs, and Photonic Interconnects, Apr. 2004, Strasbourg, France. The paper appears (unrefereed) in SPIE Proceedings Vol. 5453. An adaptive beam position control system is reported, for use in alignment correction for free-space parallel optical interconnects at the board-to-board level. A liquid-crystal spatial light modulator (SLM) displaying binary phase gratings is used as a diffractive optical element to steer the beam. The design and implementation of a feedback controller for the SLM are presented, and shown in experimental results to completely correct for step disturbances within 1 to 2 sample periods. Extension of the system to tolerate random vibrations is considered, in terms of both the required SLM technology and the design of the control algorithms. The discussion highlights some of the trade-offs in choosing components when using this technology to correct for different levels of vibration.

The main characteristics of germanium photodetectors integrated in silicon-on-insulator optical waveguides for intrachip optical interconnects are presented. The epitaxial Ge layers are grown on Si(001) by reduced-pressure chemical vapor deposition. The optical absorption of Ge layers is recorded from 1.2 to 1.7 µm and linked to the layer strain. The responsivity of an interdigitated metal-semiconductor-metal Ge photodetector has been measured. Light coupling from a slightly etched submicron rib silicon-on-insulator waveguide to a Ge photodetector is studied for two configurations: butt coupling and vertical coupling.

The two-dimensional continuous windowed Fourier transform has been shown to be effective for fringe pattern analysis in our previous work. In this paper, we first estimate the sampling intervals, using frame theory, to discretize the transform. Suitable sampling intervals are estimated as 1/σ_x and 1/σ_y, which is verified by simulations. Noise reduction using windowed Fourier frames is then investigated and compared with that using the orthogonal wavelet transform. Due to the coherence of its kernels and fringe patterns and its redundancy, windowed Fourier frames are able to reduce noise more effectively, which is verified by processing both simulated and experimental fringe patterns. The relative errors are reduced by half, in various simulations, from those with orthogonal wavelet filtering.

This paper is a revision of a paper presented at the SPIE conference on Algorithms and Systems for Optical Processing V, Jul. 2001, San Diego, California. The paper presented there appears (unrefereed) in SPIE Proceedings Vol. 4471. An encrypted digital holographic data reconstruction method with data compression is proposed. We show that the number of quantization levels of the digital hologram can be reduced. By computer simulations, we confirm that the method is especially useful for binary images. For gray-scale images, we propose a bit plane decomposition method. By this method, we show that both high reconstructed image quality and a high compression ratio can be achieved.

We discuss the design rationale and technological aspects of successfully commercially implemented development of high-precision extremely narrowband filters for solar and atmospheric applications and their use with telescopic instrumentation. The advantage of etalon-based filter technologies over other conventional approaches—such as interference filters, or birefringence filters—is also argued. Detailed consideration is given to the susceptibility of etalon-based filters to instrumental drawbacks of conventionally implemented etalons, to their high optical density (more than 5) within the rejected spectral regions as required by applications, and to practical aspects of threshold levels of light exposure during the use of these high-precision optical filters.

We have performed an experiment that compares the performance of human observers with that of a robust algorithm for the detection of targets in difficult, nonurban forward-looking infrared imagery. Our purpose was to benchmark the comparison and document performance differences for future algorithm improvement. The scale-insensitive detection algorithm, used as a benchmark by the Night Vision Electronic Sensors Directorate for algorithm evaluation, employed a combination of contrastlike features to locate targets. Detection receiver operating characteristic curves and observer-confidence analyses were used to compare human and algorithmic responses and to gain insight into differences. The test database contained ground targets, in natural clutter, whose detectability, as judged by human observers, ranged from easy to very difficult. In general, as compared with human observers, the algorithm detected most of the same targets, but correlated confidence with correct detections poorly and produced many more false alarms at any useful level of performance. Though characterizing human performance was not the intent of this study, results suggest that previous observational experience was not a strong predictor of human performance, and that combining individual human observations by majority vote significantly reduced false-alarm rates.

The objective of this research was to develop an optimal wavelength imaging system for detecting foreign fibers in the near infrared (NIR) region from 750 to 2500 nm. This method is based on the principle that different fibers have different spectral absorptions and reflectance characteristics. When subjected to a source of illumination at different wavelengths, foreign fibers present different reflectance values from those of cotton fibers. For simultaneously discriminating several types of foreign fibers from cotton, an optimal wavelength evaluation function for describing the cotton–foreign-fiber absorption discrimination was set up. Through a Fourier transform spectrometer experiment, the optimal wavelength for detecting these foreign fibers was determined and accordingly an optimal wavelength imaging system was developed. The wavelength selection experiment showed that 940 nm was the most appropriate wavelength for detection of a wide range of foreign fibers in cotton, and the 940-nm imaging system gave clear image features of these foreign fibers. The result suggests that NIR optimal wavelength imaging is a feasible and effective method to detect foreign fibers in cotton, which are currently difficult to detect.

An optical system based on Fourier transform near-infrared spectroscopy for nondestructive measurement of internal quality in intact fruit was developed. This system consisted of a light source, interferometer, fiber optical sensor, InGaAs detector, data collection card, and fruit holder. Quantification tests for sugar content (SC) and titratable acidity (TA) of 248 pear samples were carried out by using the multivariate calibration technique of partial least squares (PLS). The calibration model for SC and TA gave correlation coefficients of determination of 0.867 and 0.793, standard errors of calibration of 0.256 and 0.020, and standard errors of prediction of 0.320 and 0.019, respectively. Experimental results show that this optical system could be directly applied to fast quantification analysis for internal quality of fruits.

This paper describes an algorithm for the detection of low- and high-contrast targets in forward-looking infrared imagery while rejecting the effects of clutter and other associated detrimental factors. The proposed automatic target recognition algorithm involves two modules—a detector module and a clutter rejection module. The detection algorithm, based on morphology-based preprocessing, acts as a prescreener that selects possible candidate target regions for further analysis and places target-size markers in those preselected regions. The application of simple nonlinear grayscale operations in the proposed detection algorithm has been found to be especially suitable for real-time implementation. The clutter rejection module uses target- and background-specific information, extracted from training sample, to reduce false alarms often generated in the detection step. The application of two Mahalonobis distances, derived from target and background features of the training image, improves false-alarm rejection. Preliminary results indicate that the developed detection and clutter rejection modules exhibit excellent detection performance for both low- and high-contrast targets in complex backgrounds while ensuring a low false-alarm rate.

A novel image fusion method based on an expectation maximization (EM) algorithm and the discrete wavelet frame (DWF) transform is proposed. The registered images are first decomposed using the DWF transform, which is both aliasing-free and translation-invariant. The DWF decomposes the image signal into a multiresolution representation with both low-frequency coarse information and high-frequency detail information. The EM algorithm is used to fuse the low-frequency coarse information of the registered images. The informative importance measure is applied to fuse the high-frequency detail information of the registered images. The final fused image is obtained by taking the inverse transform of the composite multiresolution representations. Simulation results show that the proposed method outperforms the conventional image fusion methods.

We present a region-of-interest-based segmentation (ROI-S) algorithm and apply it for automatic target detection. The proposed algorithm requires no templates or a priori knowledge of the targets. An automatic ROI extraction approach based on localized texture and statistical features is used to locate targets in an IR scene without any prior knowledge of their type, exact size, and orientation. Two locally adaptive histogram-based segmentation techniques are applied to extract the target signature. The Bayes decision rule is applied for a bimodal histogram while entropic correlation is used for all other cases. Geometric and statistical features are automatically extracted for each suspected ROI. We suggest a unique variance-based metric for discriminating targets from clutter and for evaluating the probability of correct detection. The proposed system is successfully tested on several hundred single-frame IR images that contain multiple examples of military vehicles, with various sizes and brightness levels and in various background scenes and orientations. A high probability of correct detection (greater than 90%) with a low false alarm rate is achieved.

A novel copyright protection scheme for digital images based on visual cryptography and statistics is proposed. The proposed method employs sampling distribution of means and visual cryptography to achieve the requirements of robustness and security. Our method can register multiple secret images without altering the host image and can identify the rightful ownership without resorting to the original image. Moreover, the proposed method enables the secret images to be of any size regardless of the size of the host image. Finally, experimental results show that the proposed scheme can resist several common attacks.

Due to the provision of a more natural representation of a scene in the form of left and right eye views, a stereoscopic imaging system provides a more effective method for image/video display. Unfortunately the vast amount of information that must be transmitted/stored to represent a stereo image pair/video sequence, has so far hindered its use in commercial applications. However, by properly exploiting the spatial, temporal and binocular redundancy, a stereo image pair or a sequence could be compressed and transmitted through a single monocular channel's bandwidth without unduly sacrificing the perceived stereoscopic image quality. We propose a timely and novel framework to transmit stereoscopic data efficiently. We propose a timely and novel framework to transmit stereoscopic data efficiently. We present a new technique for coding stereo video sequences based on discrete wavelet transform (DWT) technology. The proposed technique particularly exploits zerotree entropy (ZTE) coding that makes use of the wavelet block concept to achieve low bit rate stereo video coding. One of the two image streams, namely, the main stream, is independently coded by a zerotree video CODEC, while the second stream, namely, the auxiliary stream, is predicted based on disparity compensation. A zerotree video CODEC subsequently codes the residual stream. We compare the performance of the proposed CODEC with a discrete cosine transform (DCT)-based, modified MPEG-2 stereo video CODEC. We show that the proposed CODEC outperforms the benchmark CODEC in coding both main and auxiliary streams.

This paper is a revision of a paper presented at the SPIE conference on Signal Processing, Senior Fusion, and Target Recognition XII, Aug. 2004, Orlando, Florida. The paper presented there appears (unrefereed) in SPIE Proceedings Vol. 5429. Bayesian networks for static as well as for dynamic cases have been the subject of a great deal of theoretical analysis and practical inference-algorithm development in the research community of artificial intelligence, machine learning, and pattern recognition. After summarizing the well-known theory of discrete and continuous Bayesian networks, we introduce an efficient reasoning scheme into hybrid Bayesian networks. In addition to illustrating the similarities between the dynamic Bayesian networks and the Kalman filter, we present a computationally efficient approach for the inference problem of hybrid dynamic Bayesian networks (HDBNs). The proposed method is based on the separation of the dynamic and static nodes, and subsequent hypercubic partitions via the decision tree algorithm. Experiments show that with high statistical confidence the novel algorithm used in the HDBN performs favorably in the trade-offs of computational complexity and accuracy performance, compared to other exact and approximate methods for applications with uncertainty in a dynamic system.

An investigation of partially coherent speckle is performed, including the effects of a pattern structure in the object plane of an imaging system. It is demonstrated that, when forming an image of a patterned rough surface into a binary photoresist, the width variations produced in the resultant pattern (also called line edge roughness) can increase as the imaging system becomes more incoherent. This unusual behavior occurs because of an interaction between the speckle produced by a rough surface and the partially coherent imaging properties of the pattern structure. It is shown that the increase in line edge roughness for a more incoherent system requires that the surface roughness of the object structure have a correlation length that is substantially smaller than the resolution of the imaging system.

A procedure for the use of the effective-index method (EIM) for high-index-contrast photonic crystal slabs (PCSs) is proposed and discussed. For such a structure, the unperturbed slab supports more than one guided mode in the vertical direction. If the EIM considering the fundamental mode only is used to deal with such a structure, large calculation errors will be introduced into the results. By comparing the gap map in the guided-mode spectrum of the hole-type PCS with those of hole-type two-dimensional photonic crystals (2-D PCs) with different refractive indices, we find that if the refractive index is selected appropriately, the agreement between these two gap maps is very good. The dispersion curves of the effective 2-D line-defect hole-type PC waveguide also agree very well with those of the line-defect hole-type PCS waveguide. However, for the pillar-type PCS, we cannot use the EIM to reduce the required calculation time and computer memory. We think that the main reason for this is the different guiding mechanisms of the optical field in these two types of PCSs.

A method to test beamsplitters using Michelson interferometer is proposed. The visibility of the interference fringes is used for the beam ratio calculations. The beam ratios of all the interfering beams at the detector plane can be determined using this method.